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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_12 / Let M be the midpoint of (AB)¯ in regular tetrahedron ABCD. (p)/(q)=cos(∠CMD) is irreducible fraction, what is the value of p+q?

Problem

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problem

Let

M

be the midpoint of

\overline{AB}

in regular tetrahedron

ABCD

\frac{p}{q}=\cos(\angle CMD)

is irreducible fraction, what is the value of

p+q

Plain-text mathematical notation (without MathML)

Let M be the midpoint of (AB)¯ in regular tetrahedron ABCD.  (p)/(q)=cos(∠CMD) is irreducible fraction, what is the value of p+q?

Original LaTeX notation

Let $M$ be the midpoint of $\overline{AB}$ in regular tetrahedron $ABCD$.  $\frac{p}{q}=\cos(\angle CMD)$ is irreducible fraction, what is the value of $p+q$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_12
task_id: d81498c1-76ef-5b1b-8750-f10bcda97ec1
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f12
task_revision_id: 2
config / split: default / train

Official source

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